Barbara put P100 into banks savings account. The account accrues a 9% interest rate compounded annually, how much money is in the account after 12 yea

Q: The rate of growth dP/dt of a population of bacteria is proportional to the square root of t, where…

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A: Rate

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Q: Evaluate the indefinite integral. (Remember 26 dz ,7 z' + 2

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Q: A cylindrical can is being filled at the rate of at =3t" , h(t) describes the height of the…

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Q: Evaluate the line integral ( 9х + 5у)da + (х — у)dy along the curve C : x = 6 cos t, y = 12 sin t…

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Q: The following table gives the sunrise and sunset times for various dates of the year in Lincroft,…

A: Note: There are multiple questions. Few questions has multiple subparts.No specific question has…

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Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to…

A: For the arc y = x2 and the range of x from 0 to 1. So, dy = 2x dx. Now,…

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Q: x²dx с. (х-1) (х?+2x+1)

A: Topic:- application of integration

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Q: The sum of one number and five times the second number is 50. A. What are the numbers so that their…

A: Let the first number be 'x' second number be 'y'. A/q  x+5y=50⇒5y=50-x⇒y=50-x5 The product of first…

Q: x+2x+3 If A = S dx then (x-6)(x²+4) I tan- 7 A is equal to 40 Inlx – 6| - In(x? + 4) + C - Inlx – 6|…

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Q: = (7, –2) am

A: Given; u=<7,-2>            v=<-4,5>

Q: ction f has the following graph: -1 4. of the following is an infinite limit? m f(r) +0+ f(x) m f(z)…

A: Topic:- limit calculus

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Q: Determine the exact area between the x-axis and the curve defined parametrically by ¤(t) = ;t2 1…

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Q: Find the partial derivatives of f(x, y) = 5x*y². %3D

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Q: aluate the integral / (8 x + 18y)dx + (24x – y)dy alor y = x² from (0, 0) to (1, 1). TE: Enter the…

A: Topic:- application of integration

Q: d Caleulate fri(t) - r(t)] and ri(e) x ra(t)] first by differentiating the product directly and then…

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: Find the exact length of the curve. =글Vy (y-3), 16 <y< 25 X =

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Q: y = zsin z

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where o sts 1. (y – x) dx +…

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Q: b. Vr4 – 2.x² + 1 dx

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Q: Find the general solution 5. (D² – 1)y = 0

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Q: cosxsin?xdx Solve using algebraic substitutionf V1+sinx

A: We have to find Integration using algebraic substitution.

Q: 2. Use the definition of integral to evaluate the integral (x³ + 1)dx. (hint: [ S(x)dx = lim Ës(x,…

A: A detailed solution is given below

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 10 cos(t)i + 11 sin(t)j +…

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Q: Find T(t) and N(t) at the given point. r(t) = 8 cos(t)i + 8 sin(t)j; t= 3 T() N(G) .3

A: To find the vectors T(t) and N(t)  for the given r(t) at point t=pi/3.

Q: t cos t?dt can best be evaluated by: A None B Trigonometric Transformation Integration by Parts…

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Q: Which integral corresponds to the area of the shaded region between the curves y = |a² – 4| and y =…

A: To find the area of the shaded region.

Q: [y sxy dy is equal to -y cony - J cony A (B у сoly - coty dy Scory dy C у coly + -y coty + J coty D…

A: Solution is given below..

Q: y" – 2y' + y = Ita² 1+x?

A: We use the method of variation of parameters

Q: 6. Evaluate - x4 dx by making a substitution and interpreting the resulting integral in terms of an…

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: What theorem is used to solve for centroid? Pappus O varignon's O Castiglliano's O Pascal's

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Q: Which integral corresponds to the volume of the solid generated by revolving the region enclosed by…

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Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 6tj – 6ik) dt

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Q: Find the exact area under the curve between the indicated values of x. y =x2 - 6x + 9; between x= 2…

A: Solution: ∫24(x2-6x+9)dx

Q: Product/Quotient/Chain Rules for Differentiation: Answer the following

A: Differentiation

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dx + 5x2y2 dy

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Q: Take

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Q: The area enclosed by the curves y = x + 2 and x is . y = 7 + 5x %3D - .... 1) 36 2) 120 3) 34 4) 118…

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Q: Verify Green's Theorem by evaluating both integrals y² dk + x² dy = / dA ay ax for the given path.…

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Q: The rate of decay of radium is proportional to the amount present at any time. The half-life of…

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Q: Find div F and curl F if F(x, y, z) = x’i – 7j + yzk. - div F= curl F=

A: Given that     F(x,y,z) = x5i - 7j + yzk